Fundamentals of Data Science Assessment Sheet
Matt Prill
Using mixture of typeset and images of workings out
See ’R Markdown and Literate programming pdf
https://ele.exeter.ac.uk/pluginfile.php/4501313/mod_resource/content/3/docs/index.html
See also Rmarkdown cheatsheet
https://raw.githubusercontent.com/rstudio/cheatsheets/main/rmarkdown.pdf
Typeset Example: Spearmans rmarkdown
\[\ r_s = 1 -\left(\frac{6\sum_{}D^2}{n(n^2-1)}\right)\]
Images
Note that you must use out.width and out.height to scale external images (fig.height and fig.width won’t work). To see images, must knit file
echo = FALSE` parameter added to prevent printing of the R code # Libraries
library(ggplot2) # For Plotting
library(dplyr) # For data manipulation
Q1
a)
Intial Equations:
\[
\Large
\begin{aligned}
x + y + z &= 1 \\
x + 2y + 4z &= \eta \\
x + 4y + 10z &= \eta^2
\end{aligned}
\]
Initial Coefficient Matrix:
\[ A = \Large \begin{bmatrix} 1 & 1 & 1 \\ 1 & 10 & 4 \\ 1 & 4 & 10 \end{bmatrix} = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \]
Identifying Eigenvalues:
\[ \Large \begin{bmatrix} 1 - \lambda & 1 & 1 \\ 1 & 10 - \lambda & 4 \\ 1 & 4 & 10 - \lambda \end{bmatrix} \]